Moment of Inertia, and Stress Area.
To find the Moment of Inertia of any Beam Section.
-Proceed as in the last construction and find Z.
nd I = Zjy.* So for rectangular sections
bJP h ^bh*
Then Z = -
Stress areas for circle, hollow circle, triangle, and hollow
•ectangle we shewn in Fig. 385, being measured as in Fig. 372
mean width x - Y The centre of gravity of each area is obtained
y cutting out in stiff paper and hanging up in two different
,|tf_ - .....O —— —- —y
>ositions to mark two plumb lines, which will cross at G. For
he triangular beam the neutral axis must be drawn at ^ the
leight, a line of limiting stress drawn across the apex, and another
>elow, at an equal distance from its axis. Projecting and con-
urging, we shall obtain the areas shewn, which must be equal.
The results are as follows :
Moment of resistance of circle =f'og82 d*
of hollow circle =7-0982 :
of hollow rectangle =7'1666:
* See also note, page 430; see also page 845.